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Mathematical analysis of delay differential equation models of HIV-1 infection. (English) Zbl 0992.92035
Summary: Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, $\delta$, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of $\delta$. We also provide some general results on the stability of non-linear delay differential equation infection models.

##### MSC:
 92C60 Medical epidemiology 34K20 Stability theory of functional-differential equations 92C50 Medical applications of mathematical biology 92D30 Epidemiology